Reputation level bonuses are what you get when you reach that level of reputation with a faction. These stack from 0 up, or 0 down, depending on your reputation level. These aren't listed in the game book as it is an optional component.
When you move into a settlement you don't roll for an encounter. There are no Settlement Encounters at this time.
When a faction grows they do so from each settlement they control, just as you have mentioned.